UCL - Optimization : Nonlinear programming

[INMA2460]

[30h + 22.5h] 5 credits

This course is taught in the 1st semester.

Teacher(s): Yurii Nesterov

Language: English

Level: Second

Aims
Main themes
Content and teaching methods
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

Introduce a modern theory of optimization and general principles of complexity analysis of algorithms for solving nonlinear problems. Present the most efficient algorithmic schemes.

Main themes

General nonlinear optimization. Smooth and non-smooth convex optimization. Interior-point methods. Prerequisites: standard undergraduate level in Linear Algebra and Calculus.

Content and teaching methods

-General problem of nonlinear optimization. Black-box concept. Iterative methods and analytical complexity. Gradient method and Newton method. Local complexity analysis.
-Convex optimization: convex sets and functions; minimization of differentiable and non-differentiable convex functions; lower complexity bounds; optimal methods.
-Interior-point methods: notion of self-concordant functions and barriers; path-following methods; structural optimization.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

- copy of transparencies and of the text of the lectures.
- Yu.Nesterov. "Introductory lectures on convex optimization. Basic course." Kluwer 2003
- P. Polyak, « Introduction in optimization », J. Willey & Sons, 1989

- Yu. Nesterov, A. Nemirovsky, « Interior-point polynomial algorithms in nonlinear optimization », SIAM, Philadelphia, 1994.

The course is given in English.
Evaluation: a written exam (in French or in English).